Model Acquisition Using Shape-from-Shading

In this paper we show how the Mumford-Shah functional can be used to derive diffusion kernels that can be employed in the recovery of surface height in shape-from-shading. We commence from an initial field of surface normals which are constrained to fall on the Lambertian reflectance cone and to point in the direction of the local Canny edge gradient. We aim to find a path through this field of surface normals which can be used for surface height reconstruction. We demonstrate that the Mumford-Shah functional leads to a diffusion process which is a Markov chain on the field of surface normals. We find the steady state of the Markov chain using the leading eigenvector for the transition probability matrix computed from the diffusion kernels. We show how the steady state path can be used for height recovery and also for smoothing the initial field of surface normals.

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